Was actually looking at heat(/hot air) gun prices myself yesterday because i'll be doing some braiding myself soon.
Check Wickes and Homebase, they both do lower end heatguns and you should be able to find one with a reducer attachment for pretty cheap(reducer will direct the heat through a smaller nozzle, so you don't end up putting heat over too large an area - you specifically want heat in a smaller area if you're heatshrinking). Bear in mind a lot of them will come without any attachments and often charge a fair bit to buy them seperately(so check the product description on items you're looking at, ideal if you can get a reducer/spot nozzle included).
£10 - £20 if you shop around and you should be able to pick one up in either of the above mentioned stores(not competitors, they don't sell PC hardware), or somewhere local(no need to have anything delivered, that's more cost).
I've tried the lighter route before, it's not fun and it's far to easy to mess up or blacken the heatshrink(told myself last time, never again until i have a heatgun).